| @@ -1,194 +0,0 @@ | |||
| SUBROUTINE CGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) | |||
| * | |||
| * -- LAPACK routine (version 3.0) -- | |||
| * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., | |||
| * Courant Institute, Argonne National Lab, and Rice University | |||
| * June 30, 1999 | |||
| * | |||
| * .. Scalar Arguments .. | |||
| INTEGER INFO, LDA, LWORK, N | |||
| * .. | |||
| * .. Array Arguments .. | |||
| INTEGER IPIV( * ) | |||
| COMPLEX A( LDA, * ), WORK( * ) | |||
| * .. | |||
| * | |||
| * Purpose | |||
| * ======= | |||
| * | |||
| * CGETRI computes the inverse of a matrix using the LU factorization | |||
| * computed by CGETRF. | |||
| * | |||
| * This method inverts U and then computes inv(A) by solving the system | |||
| * inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| * Arguments | |||
| * ========= | |||
| * | |||
| * N (input) INTEGER | |||
| * The order of the matrix A. N >= 0. | |||
| * | |||
| * A (input/output) COMPLEX array, dimension (LDA,N) | |||
| * On entry, the factors L and U from the factorization | |||
| * A = P*L*U as computed by CGETRF. | |||
| * On exit, if INFO = 0, the inverse of the original matrix A. | |||
| * | |||
| * LDA (input) INTEGER | |||
| * The leading dimension of the array A. LDA >= max(1,N). | |||
| * | |||
| * IPIV (input) INTEGER array, dimension (N) | |||
| * The pivot indices from CGETRF; for 1<=i<=N, row i of the | |||
| * matrix was interchanged with row IPIV(i). | |||
| * | |||
| * WORK (workspace/output) COMPLEX array, dimension (LWORK) | |||
| * On exit, if INFO=0, then WORK(1) returns the optimal LWORK. | |||
| * | |||
| * LWORK (input) INTEGER | |||
| * The dimension of the array WORK. LWORK >= max(1,N). | |||
| * For optimal performance LWORK >= N*NB, where NB is | |||
| * the optimal blocksize returned by ILAENV. | |||
| * | |||
| * If LWORK = -1, then a workspace query is assumed; the routine | |||
| * only calculates the optimal size of the WORK array, returns | |||
| * this value as the first entry of the WORK array, and no error | |||
| * message related to LWORK is issued by XERBLA. | |||
| * | |||
| * INFO (output) INTEGER | |||
| * = 0: successful exit | |||
| * < 0: if INFO = -i, the i-th argument had an illegal value | |||
| * > 0: if INFO = i, U(i,i) is exactly zero; the matrix is | |||
| * singular and its inverse could not be computed. | |||
| * | |||
| * ===================================================================== | |||
| * | |||
| * .. Parameters .. | |||
| COMPLEX ZERO, ONE | |||
| PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ), | |||
| $ ONE = ( 1.0E+0, 0.0E+0 ) ) | |||
| * .. | |||
| * .. Local Scalars .. | |||
| LOGICAL LQUERY | |||
| INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, | |||
| $ NBMIN, NN | |||
| * .. | |||
| * .. External Functions .. | |||
| INTEGER ILAENV | |||
| EXTERNAL ILAENV | |||
| * .. | |||
| * .. External Subroutines .. | |||
| EXTERNAL CGEMM, CGEMV, CSWAP, CTRSM, CTRTRI, XERBLA | |||
| * .. | |||
| * .. Intrinsic Functions .. | |||
| INTRINSIC MAX, MIN | |||
| * .. | |||
| * .. Executable Statements .. | |||
| * | |||
| * Test the input parameters. | |||
| * | |||
| INFO = 0 | |||
| NB = ILAENV( 1, 'CGETRI', ' ', N, -1, -1, -1 ) | |||
| LWKOPT = N*NB | |||
| WORK( 1 ) = LWKOPT | |||
| LQUERY = ( LWORK.EQ.-1 ) | |||
| IF( N.LT.0 ) THEN | |||
| INFO = -1 | |||
| ELSE IF( LDA.LT.MAX( 1, N ) ) THEN | |||
| INFO = -3 | |||
| ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN | |||
| INFO = -6 | |||
| END IF | |||
| IF( INFO.NE.0 ) THEN | |||
| CALL XERBLA( 'CGETRI', -INFO ) | |||
| RETURN | |||
| ELSE IF( LQUERY ) THEN | |||
| RETURN | |||
| END IF | |||
| * | |||
| * Quick return if possible | |||
| * | |||
| IF( N.EQ.0 ) | |||
| $ RETURN | |||
| * | |||
| * Form inv(U). If INFO > 0 from CTRTRI, then U is singular, | |||
| * and the inverse is not computed. | |||
| * | |||
| CALL CTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) | |||
| IF( INFO.GT.0 ) | |||
| $ RETURN | |||
| * | |||
| NBMIN = 2 | |||
| LDWORK = N | |||
| IF( NB.GT.1 .AND. NB.LT.N ) THEN | |||
| IWS = MAX( LDWORK*NB, 1 ) | |||
| IF( LWORK.LT.IWS ) THEN | |||
| NB = LWORK / LDWORK | |||
| NBMIN = MAX( 2, ILAENV( 2, 'CGETRI', ' ', N, -1, -1, -1 ) ) | |||
| END IF | |||
| ELSE | |||
| IWS = N | |||
| END IF | |||
| * | |||
| * Solve the equation inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN | |||
| * | |||
| * Use unblocked code. | |||
| * | |||
| DO 20 J = N, 1, -1 | |||
| * | |||
| * Copy current column of L to WORK and replace with zeros. | |||
| * | |||
| DO 10 I = J + 1, N | |||
| WORK( I ) = A( I, J ) | |||
| A( I, J ) = ZERO | |||
| 10 CONTINUE | |||
| * | |||
| * Compute current column of inv(A). | |||
| * | |||
| IF( J.LT.N ) | |||
| $ CALL CGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), | |||
| $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) | |||
| 20 CONTINUE | |||
| ELSE | |||
| * | |||
| * Use blocked code. | |||
| * | |||
| NN = ( ( N-1 ) / NB )*NB + 1 | |||
| DO 50 J = NN, 1, -NB | |||
| JB = MIN( NB, N-J+1 ) | |||
| * | |||
| * Copy current block column of L to WORK and replace with | |||
| * zeros. | |||
| * | |||
| DO 40 JJ = J, J + JB - 1 | |||
| DO 30 I = JJ + 1, N | |||
| WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) | |||
| A( I, JJ ) = ZERO | |||
| 30 CONTINUE | |||
| 40 CONTINUE | |||
| * | |||
| * Compute current block column of inv(A). | |||
| * | |||
| IF( J+JB.LE.N ) | |||
| $ CALL CGEMM( 'No transpose', 'No transpose', N, JB, | |||
| $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, | |||
| $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) | |||
| CALL CTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, | |||
| $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) | |||
| 50 CONTINUE | |||
| END IF | |||
| * | |||
| * Apply column interchanges. | |||
| * | |||
| DO 60 J = N - 1, 1, -1 | |||
| JP = IPIV( J ) | |||
| IF( JP.NE.J ) | |||
| $ CALL CSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) | |||
| 60 CONTINUE | |||
| * | |||
| WORK( 1 ) = IWS | |||
| RETURN | |||
| * | |||
| * End of CGETRI | |||
| * | |||
| END | |||
| @@ -1,193 +0,0 @@ | |||
| SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) | |||
| * | |||
| * -- LAPACK routine (version 3.0) -- | |||
| * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., | |||
| * Courant Institute, Argonne National Lab, and Rice University | |||
| * June 30, 1999 | |||
| * | |||
| * .. Scalar Arguments .. | |||
| INTEGER INFO, LDA, LWORK, N | |||
| * .. | |||
| * .. Array Arguments .. | |||
| INTEGER IPIV( * ) | |||
| DOUBLE PRECISION A( LDA, * ), WORK( * ) | |||
| * .. | |||
| * | |||
| * Purpose | |||
| * ======= | |||
| * | |||
| * DGETRI computes the inverse of a matrix using the LU factorization | |||
| * computed by DGETRF. | |||
| * | |||
| * This method inverts U and then computes inv(A) by solving the system | |||
| * inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| * Arguments | |||
| * ========= | |||
| * | |||
| * N (input) INTEGER | |||
| * The order of the matrix A. N >= 0. | |||
| * | |||
| * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) | |||
| * On entry, the factors L and U from the factorization | |||
| * A = P*L*U as computed by DGETRF. | |||
| * On exit, if INFO = 0, the inverse of the original matrix A. | |||
| * | |||
| * LDA (input) INTEGER | |||
| * The leading dimension of the array A. LDA >= max(1,N). | |||
| * | |||
| * IPIV (input) INTEGER array, dimension (N) | |||
| * The pivot indices from DGETRF; for 1<=i<=N, row i of the | |||
| * matrix was interchanged with row IPIV(i). | |||
| * | |||
| * WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) | |||
| * On exit, if INFO=0, then WORK(1) returns the optimal LWORK. | |||
| * | |||
| * LWORK (input) INTEGER | |||
| * The dimension of the array WORK. LWORK >= max(1,N). | |||
| * For optimal performance LWORK >= N*NB, where NB is | |||
| * the optimal blocksize returned by ILAENV. | |||
| * | |||
| * If LWORK = -1, then a workspace query is assumed; the routine | |||
| * only calculates the optimal size of the WORK array, returns | |||
| * this value as the first entry of the WORK array, and no error | |||
| * message related to LWORK is issued by XERBLA. | |||
| * | |||
| * INFO (output) INTEGER | |||
| * = 0: successful exit | |||
| * < 0: if INFO = -i, the i-th argument had an illegal value | |||
| * > 0: if INFO = i, U(i,i) is exactly zero; the matrix is | |||
| * singular and its inverse could not be computed. | |||
| * | |||
| * ===================================================================== | |||
| * | |||
| * .. Parameters .. | |||
| DOUBLE PRECISION ZERO, ONE | |||
| PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) | |||
| * .. | |||
| * .. Local Scalars .. | |||
| LOGICAL LQUERY | |||
| INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, | |||
| $ NBMIN, NN | |||
| * .. | |||
| * .. External Functions .. | |||
| INTEGER ILAENV | |||
| EXTERNAL ILAENV | |||
| * .. | |||
| * .. External Subroutines .. | |||
| EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA | |||
| * .. | |||
| * .. Intrinsic Functions .. | |||
| INTRINSIC MAX, MIN | |||
| * .. | |||
| * .. Executable Statements .. | |||
| * | |||
| * Test the input parameters. | |||
| * | |||
| INFO = 0 | |||
| NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 ) | |||
| LWKOPT = N*NB | |||
| WORK( 1 ) = LWKOPT | |||
| LQUERY = ( LWORK.EQ.-1 ) | |||
| IF( N.LT.0 ) THEN | |||
| INFO = -1 | |||
| ELSE IF( LDA.LT.MAX( 1, N ) ) THEN | |||
| INFO = -3 | |||
| ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN | |||
| INFO = -6 | |||
| END IF | |||
| IF( INFO.NE.0 ) THEN | |||
| CALL XERBLA( 'DGETRI', -INFO ) | |||
| RETURN | |||
| ELSE IF( LQUERY ) THEN | |||
| RETURN | |||
| END IF | |||
| * | |||
| * Quick return if possible | |||
| * | |||
| IF( N.EQ.0 ) | |||
| $ RETURN | |||
| * | |||
| * Form inv(U). If INFO > 0 from DTRTRI, then U is singular, | |||
| * and the inverse is not computed. | |||
| * | |||
| CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) | |||
| IF( INFO.GT.0 ) | |||
| $ RETURN | |||
| * | |||
| NBMIN = 2 | |||
| LDWORK = N | |||
| IF( NB.GT.1 .AND. NB.LT.N ) THEN | |||
| IWS = MAX( LDWORK*NB, 1 ) | |||
| IF( LWORK.LT.IWS ) THEN | |||
| NB = LWORK / LDWORK | |||
| NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) ) | |||
| END IF | |||
| ELSE | |||
| IWS = N | |||
| END IF | |||
| * | |||
| * Solve the equation inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN | |||
| * | |||
| * Use unblocked code. | |||
| * | |||
| DO 20 J = N, 1, -1 | |||
| * | |||
| * Copy current column of L to WORK and replace with zeros. | |||
| * | |||
| DO 10 I = J + 1, N | |||
| WORK( I ) = A( I, J ) | |||
| A( I, J ) = ZERO | |||
| 10 CONTINUE | |||
| * | |||
| * Compute current column of inv(A). | |||
| * | |||
| IF( J.LT.N ) | |||
| $ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), | |||
| $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) | |||
| 20 CONTINUE | |||
| ELSE | |||
| * | |||
| * Use blocked code. | |||
| * | |||
| NN = ( ( N-1 ) / NB )*NB + 1 | |||
| DO 50 J = NN, 1, -NB | |||
| JB = MIN( NB, N-J+1 ) | |||
| * | |||
| * Copy current block column of L to WORK and replace with | |||
| * zeros. | |||
| * | |||
| DO 40 JJ = J, J + JB - 1 | |||
| DO 30 I = JJ + 1, N | |||
| WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) | |||
| A( I, JJ ) = ZERO | |||
| 30 CONTINUE | |||
| 40 CONTINUE | |||
| * | |||
| * Compute current block column of inv(A). | |||
| * | |||
| IF( J+JB.LE.N ) | |||
| $ CALL DGEMM( 'No transpose', 'No transpose', N, JB, | |||
| $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, | |||
| $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) | |||
| CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, | |||
| $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) | |||
| 50 CONTINUE | |||
| END IF | |||
| * | |||
| * Apply column interchanges. | |||
| * | |||
| DO 60 J = N - 1, 1, -1 | |||
| JP = IPIV( J ) | |||
| IF( JP.NE.J ) | |||
| $ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) | |||
| 60 CONTINUE | |||
| * | |||
| WORK( 1 ) = IWS | |||
| RETURN | |||
| * | |||
| * End of DGETRI | |||
| * | |||
| END | |||
| @@ -1,193 +0,0 @@ | |||
| SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) | |||
| * | |||
| * -- LAPACK routine (version 3.0) -- | |||
| * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., | |||
| * Courant Institute, Argonne National Lab, and Rice University | |||
| * June 30, 1999 | |||
| * | |||
| * .. Scalar Arguments .. | |||
| INTEGER INFO, LDA, LWORK, N | |||
| * .. | |||
| * .. Array Arguments .. | |||
| INTEGER IPIV( * ) | |||
| REAL A( LDA, * ), WORK( * ) | |||
| * .. | |||
| * | |||
| * Purpose | |||
| * ======= | |||
| * | |||
| * SGETRI computes the inverse of a matrix using the LU factorization | |||
| * computed by SGETRF. | |||
| * | |||
| * This method inverts U and then computes inv(A) by solving the system | |||
| * inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| * Arguments | |||
| * ========= | |||
| * | |||
| * N (input) INTEGER | |||
| * The order of the matrix A. N >= 0. | |||
| * | |||
| * A (input/output) REAL array, dimension (LDA,N) | |||
| * On entry, the factors L and U from the factorization | |||
| * A = P*L*U as computed by SGETRF. | |||
| * On exit, if INFO = 0, the inverse of the original matrix A. | |||
| * | |||
| * LDA (input) INTEGER | |||
| * The leading dimension of the array A. LDA >= max(1,N). | |||
| * | |||
| * IPIV (input) INTEGER array, dimension (N) | |||
| * The pivot indices from SGETRF; for 1<=i<=N, row i of the | |||
| * matrix was interchanged with row IPIV(i). | |||
| * | |||
| * WORK (workspace/output) REAL array, dimension (LWORK) | |||
| * On exit, if INFO=0, then WORK(1) returns the optimal LWORK. | |||
| * | |||
| * LWORK (input) INTEGER | |||
| * The dimension of the array WORK. LWORK >= max(1,N). | |||
| * For optimal performance LWORK >= N*NB, where NB is | |||
| * the optimal blocksize returned by ILAENV. | |||
| * | |||
| * If LWORK = -1, then a workspace query is assumed; the routine | |||
| * only calculates the optimal size of the WORK array, returns | |||
| * this value as the first entry of the WORK array, and no error | |||
| * message related to LWORK is issued by XERBLA. | |||
| * | |||
| * INFO (output) INTEGER | |||
| * = 0: successful exit | |||
| * < 0: if INFO = -i, the i-th argument had an illegal value | |||
| * > 0: if INFO = i, U(i,i) is exactly zero; the matrix is | |||
| * singular and its inverse could not be computed. | |||
| * | |||
| * ===================================================================== | |||
| * | |||
| * .. Parameters .. | |||
| REAL ZERO, ONE | |||
| PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) | |||
| * .. | |||
| * .. Local Scalars .. | |||
| LOGICAL LQUERY | |||
| INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, | |||
| $ NBMIN, NN | |||
| * .. | |||
| * .. External Functions .. | |||
| INTEGER ILAENV | |||
| EXTERNAL ILAENV | |||
| * .. | |||
| * .. External Subroutines .. | |||
| EXTERNAL SGEMM, SGEMV, SSWAP, STRSM, STRTRI, XERBLA | |||
| * .. | |||
| * .. Intrinsic Functions .. | |||
| INTRINSIC MAX, MIN | |||
| * .. | |||
| * .. Executable Statements .. | |||
| * | |||
| * Test the input parameters. | |||
| * | |||
| INFO = 0 | |||
| NB = ILAENV( 1, 'SGETRI', ' ', N, -1, -1, -1 ) | |||
| LWKOPT = N*NB | |||
| WORK( 1 ) = LWKOPT | |||
| LQUERY = ( LWORK.EQ.-1 ) | |||
| IF( N.LT.0 ) THEN | |||
| INFO = -1 | |||
| ELSE IF( LDA.LT.MAX( 1, N ) ) THEN | |||
| INFO = -3 | |||
| ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN | |||
| INFO = -6 | |||
| END IF | |||
| IF( INFO.NE.0 ) THEN | |||
| CALL XERBLA( 'SGETRI', -INFO ) | |||
| RETURN | |||
| ELSE IF( LQUERY ) THEN | |||
| RETURN | |||
| END IF | |||
| * | |||
| * Quick return if possible | |||
| * | |||
| IF( N.EQ.0 ) | |||
| $ RETURN | |||
| * | |||
| * Form inv(U). If INFO > 0 from STRTRI, then U is singular, | |||
| * and the inverse is not computed. | |||
| * | |||
| CALL STRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) | |||
| IF( INFO.GT.0 ) | |||
| $ RETURN | |||
| * | |||
| NBMIN = 2 | |||
| LDWORK = N | |||
| IF( NB.GT.1 .AND. NB.LT.N ) THEN | |||
| IWS = MAX( LDWORK*NB, 1 ) | |||
| IF( LWORK.LT.IWS ) THEN | |||
| NB = LWORK / LDWORK | |||
| NBMIN = MAX( 2, ILAENV( 2, 'SGETRI', ' ', N, -1, -1, -1 ) ) | |||
| END IF | |||
| ELSE | |||
| IWS = N | |||
| END IF | |||
| * | |||
| * Solve the equation inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN | |||
| * | |||
| * Use unblocked code. | |||
| * | |||
| DO 20 J = N, 1, -1 | |||
| * | |||
| * Copy current column of L to WORK and replace with zeros. | |||
| * | |||
| DO 10 I = J + 1, N | |||
| WORK( I ) = A( I, J ) | |||
| A( I, J ) = ZERO | |||
| 10 CONTINUE | |||
| * | |||
| * Compute current column of inv(A). | |||
| * | |||
| IF( J.LT.N ) | |||
| $ CALL SGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), | |||
| $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) | |||
| 20 CONTINUE | |||
| ELSE | |||
| * | |||
| * Use blocked code. | |||
| * | |||
| NN = ( ( N-1 ) / NB )*NB + 1 | |||
| DO 50 J = NN, 1, -NB | |||
| JB = MIN( NB, N-J+1 ) | |||
| * | |||
| * Copy current block column of L to WORK and replace with | |||
| * zeros. | |||
| * | |||
| DO 40 JJ = J, J + JB - 1 | |||
| DO 30 I = JJ + 1, N | |||
| WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) | |||
| A( I, JJ ) = ZERO | |||
| 30 CONTINUE | |||
| 40 CONTINUE | |||
| * | |||
| * Compute current block column of inv(A). | |||
| * | |||
| IF( J+JB.LE.N ) | |||
| $ CALL SGEMM( 'No transpose', 'No transpose', N, JB, | |||
| $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, | |||
| $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) | |||
| CALL STRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, | |||
| $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) | |||
| 50 CONTINUE | |||
| END IF | |||
| * | |||
| * Apply column interchanges. | |||
| * | |||
| DO 60 J = N - 1, 1, -1 | |||
| JP = IPIV( J ) | |||
| IF( JP.NE.J ) | |||
| $ CALL SSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) | |||
| 60 CONTINUE | |||
| * | |||
| WORK( 1 ) = IWS | |||
| RETURN | |||
| * | |||
| * End of SGETRI | |||
| * | |||
| END | |||
| @@ -1,194 +0,0 @@ | |||
| SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) | |||
| * | |||
| * -- LAPACK routine (version 3.0) -- | |||
| * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., | |||
| * Courant Institute, Argonne National Lab, and Rice University | |||
| * June 30, 1999 | |||
| * | |||
| * .. Scalar Arguments .. | |||
| INTEGER INFO, LDA, LWORK, N | |||
| * .. | |||
| * .. Array Arguments .. | |||
| INTEGER IPIV( * ) | |||
| COMPLEX*16 A( LDA, * ), WORK( * ) | |||
| * .. | |||
| * | |||
| * Purpose | |||
| * ======= | |||
| * | |||
| * ZGETRI computes the inverse of a matrix using the LU factorization | |||
| * computed by ZGETRF. | |||
| * | |||
| * This method inverts U and then computes inv(A) by solving the system | |||
| * inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| * Arguments | |||
| * ========= | |||
| * | |||
| * N (input) INTEGER | |||
| * The order of the matrix A. N >= 0. | |||
| * | |||
| * A (input/output) COMPLEX*16 array, dimension (LDA,N) | |||
| * On entry, the factors L and U from the factorization | |||
| * A = P*L*U as computed by ZGETRF. | |||
| * On exit, if INFO = 0, the inverse of the original matrix A. | |||
| * | |||
| * LDA (input) INTEGER | |||
| * The leading dimension of the array A. LDA >= max(1,N). | |||
| * | |||
| * IPIV (input) INTEGER array, dimension (N) | |||
| * The pivot indices from ZGETRF; for 1<=i<=N, row i of the | |||
| * matrix was interchanged with row IPIV(i). | |||
| * | |||
| * WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) | |||
| * On exit, if INFO=0, then WORK(1) returns the optimal LWORK. | |||
| * | |||
| * LWORK (input) INTEGER | |||
| * The dimension of the array WORK. LWORK >= max(1,N). | |||
| * For optimal performance LWORK >= N*NB, where NB is | |||
| * the optimal blocksize returned by ILAENV. | |||
| * | |||
| * If LWORK = -1, then a workspace query is assumed; the routine | |||
| * only calculates the optimal size of the WORK array, returns | |||
| * this value as the first entry of the WORK array, and no error | |||
| * message related to LWORK is issued by XERBLA. | |||
| * | |||
| * INFO (output) INTEGER | |||
| * = 0: successful exit | |||
| * < 0: if INFO = -i, the i-th argument had an illegal value | |||
| * > 0: if INFO = i, U(i,i) is exactly zero; the matrix is | |||
| * singular and its inverse could not be computed. | |||
| * | |||
| * ===================================================================== | |||
| * | |||
| * .. Parameters .. | |||
| COMPLEX*16 ZERO, ONE | |||
| PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), | |||
| $ ONE = ( 1.0D+0, 0.0D+0 ) ) | |||
| * .. | |||
| * .. Local Scalars .. | |||
| LOGICAL LQUERY | |||
| INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, | |||
| $ NBMIN, NN | |||
| * .. | |||
| * .. External Functions .. | |||
| INTEGER ILAENV | |||
| EXTERNAL ILAENV | |||
| * .. | |||
| * .. External Subroutines .. | |||
| EXTERNAL XERBLA, ZGEMM, ZGEMV, ZSWAP, ZTRSM, ZTRTRI | |||
| * .. | |||
| * .. Intrinsic Functions .. | |||
| INTRINSIC MAX, MIN | |||
| * .. | |||
| * .. Executable Statements .. | |||
| * | |||
| * Test the input parameters. | |||
| * | |||
| INFO = 0 | |||
| NB = ILAENV( 1, 'ZGETRI', ' ', N, -1, -1, -1 ) | |||
| LWKOPT = N*NB | |||
| WORK( 1 ) = LWKOPT | |||
| LQUERY = ( LWORK.EQ.-1 ) | |||
| IF( N.LT.0 ) THEN | |||
| INFO = -1 | |||
| ELSE IF( LDA.LT.MAX( 1, N ) ) THEN | |||
| INFO = -3 | |||
| ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN | |||
| INFO = -6 | |||
| END IF | |||
| IF( INFO.NE.0 ) THEN | |||
| CALL XERBLA( 'ZGETRI', -INFO ) | |||
| RETURN | |||
| ELSE IF( LQUERY ) THEN | |||
| RETURN | |||
| END IF | |||
| * | |||
| * Quick return if possible | |||
| * | |||
| IF( N.EQ.0 ) | |||
| $ RETURN | |||
| * | |||
| * Form inv(U). If INFO > 0 from ZTRTRI, then U is singular, | |||
| * and the inverse is not computed. | |||
| * | |||
| CALL ZTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) | |||
| IF( INFO.GT.0 ) | |||
| $ RETURN | |||
| * | |||
| NBMIN = 2 | |||
| LDWORK = N | |||
| IF( NB.GT.1 .AND. NB.LT.N ) THEN | |||
| IWS = MAX( LDWORK*NB, 1 ) | |||
| IF( LWORK.LT.IWS ) THEN | |||
| NB = LWORK / LDWORK | |||
| NBMIN = MAX( 2, ILAENV( 2, 'ZGETRI', ' ', N, -1, -1, -1 ) ) | |||
| END IF | |||
| ELSE | |||
| IWS = N | |||
| END IF | |||
| * | |||
| * Solve the equation inv(A)*L = inv(U) for inv(A). | |||
| * | |||
| IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN | |||
| * | |||
| * Use unblocked code. | |||
| * | |||
| DO 20 J = N, 1, -1 | |||
| * | |||
| * Copy current column of L to WORK and replace with zeros. | |||
| * | |||
| DO 10 I = J + 1, N | |||
| WORK( I ) = A( I, J ) | |||
| A( I, J ) = ZERO | |||
| 10 CONTINUE | |||
| * | |||
| * Compute current column of inv(A). | |||
| * | |||
| IF( J.LT.N ) | |||
| $ CALL ZGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), | |||
| $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) | |||
| 20 CONTINUE | |||
| ELSE | |||
| * | |||
| * Use blocked code. | |||
| * | |||
| NN = ( ( N-1 ) / NB )*NB + 1 | |||
| DO 50 J = NN, 1, -NB | |||
| JB = MIN( NB, N-J+1 ) | |||
| * | |||
| * Copy current block column of L to WORK and replace with | |||
| * zeros. | |||
| * | |||
| DO 40 JJ = J, J + JB - 1 | |||
| DO 30 I = JJ + 1, N | |||
| WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) | |||
| A( I, JJ ) = ZERO | |||
| 30 CONTINUE | |||
| 40 CONTINUE | |||
| * | |||
| * Compute current block column of inv(A). | |||
| * | |||
| IF( J+JB.LE.N ) | |||
| $ CALL ZGEMM( 'No transpose', 'No transpose', N, JB, | |||
| $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, | |||
| $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) | |||
| CALL ZTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, | |||
| $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) | |||
| 50 CONTINUE | |||
| END IF | |||
| * | |||
| * Apply column interchanges. | |||
| * | |||
| DO 60 J = N - 1, 1, -1 | |||
| JP = IPIV( J ) | |||
| IF( JP.NE.J ) | |||
| $ CALL ZSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) | |||
| 60 CONTINUE | |||
| * | |||
| WORK( 1 ) = IWS | |||
| RETURN | |||
| * | |||
| * End of ZGETRI | |||
| * | |||
| END | |||